Be Afraid, Be Very Very Afraid

Two for the price of one today:

1)  First, in time for Halloween, DO NOT miss the frightful tale of Differentiation... as only Ben Orlin can tell it (bwaaahaaaahaaaaa):
http://mathwithbaddrawings.com/2015/10/28/the-differentiation-a-survivors-tale/


2)  Less scary, but more mind-racking perhaps than differentiation, is the 'Sleeping Beauty Problem/Paradox,' which I haven't mentioned for awhile, but do now (...at least one version of it):



The correct answer is: 1/2, 1/3?; 1/2, 1/3?; 1/2 or 1/3???.... two different logical answers, splitting the mind in two, with no final resolution. Spine-tingling stuff! ;-)
My original post on it was back in 2012 with a number of additional links:
http://math-frolic.blogspot.com/2012/03/sleeping-beautynot-your-childhood-fairy.html

Also, Tanya Khovanova had lengthy previous discussion of it on her blog here:
http://blog.tanyakhovanova.com/2011/08/the-sleeping-beauty-problem/

And even physicist Sean Carroll covered it a year ago, drawing 240+ comments:
http://www.preposterousuniverse.com/blog/2014/07/28/quantum-sleeping-beauty-and-the-multiverse/

Pick your side... you'll find some good arguments (and thinkers) backing you up either way.  Spooky indeed!